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Fast and robust unsupervised identification of MS lesion change using statistical detection of changes (SDC) algorithm
Thanh D Nguyen1, Shun Zhang1, Ajay Gupta1, Susan A Gauthier1, and Yi Wang1

1Weill Cornell Medical College, New York, NY, United States

### Synopsis

The objective of this study was to develop a robust automated lesion change detection algorithm for MS. Our preliminary results in 30 patients show that our SDC algorithm achieves much higher sensitivity and specificity (99%/76%) compared to that obtained with off-the-shelf LPA algorithm (76%/27%).

### INTRODUCTION

MS patients are monitored regularly using MRI. Currently, radiologists compare hundreds of images to detect changes on consecutive scans, which is time-consuming. A fully automated lesion segmentation algorithm is desired (1). Lesion changes can be sensitively detected on subtraction images by humans (2-3) or with the help of automated algorithms relying on the signal difference and geometric constraints (4). Here we propose a robust and fast statistical detection of changes (SDC) algorithm to optimally detect lesion change using the Neyman-Pearson detector in statistics.

### METHODS

Lesion detection algorithm. Given two images I1 and I2, the signal change d=I2-I1 at voxel i is assumed to have Gaussian noise with mean µ and standard deviation σ, and SDC is formulated as a composite hypothesis test between two hypotheses: H0 ~ N(0,σ2) and H1 ~ N(µ,σ2), where N is the normal distribution and µ≠0 is unknown mean. σ can be estimated from the brain WM mask extracted from T1-weighted image with exclusion of large lesions (Fig.1). Assuming µ>0 (positive change), the test statistic can be derived from the log-likelihood ratio test: ti = $\sum_{j=1}^N$ dij where N is the number of observations at voxel i. The test statistic is then compared with a threshold γ chosen to control the probability of false positives: PFP = P(t ≥ γ | H0). This test provides the best detection power for a given PFP regardless of the unknown µ (uniformly most powerful detector) (5).

Since only one observation di is available per voxel, we propose to compute the test statistic ti = max(tk,k $\in$ Ti) where Ti denotes a 3-neighborhood system of voxel i (Fig.2) purposely chosen to match the currently accepted minimum lesion size requirement of 3 mm (3 voxels in 1 mm isotropic images) (6). Intuitively, this test statistic encodes in probabilistic terms the expectation that a bright voxel on the subtraction image is more likely considered “changed” if at least two of its neighbor voxels also have relatively high signals.

MRI experiments. Thirty MS patients underwent 3T MRI twice (interval 267±104 days, range 15-410 days). FLAIR images were automatically co-registered in the halfway space (7). The test statistic for FLAIR subtraction image was computed and thresholded to generate the change mask (Fig.1). A false positive rate PFP of 0.0001 was chosen to achieve high lesion sensitivity, which means that about 50/500,000 WM voxels may be incorrectly labeled as “changed”. To reduce the number of false positives, constraints were imposed on lesion size (≥3 voxels), location (lesions within 2 voxels of CSF border has to be connected to a lesion outside), and intensity on 2nd FLAIR (>2 standard deviations above mean).

For comparison, LPA (http:// www.applied-statistics.de) (8) was used to compute the lesion masks for FLAIR images with mask subtraction as a change mask. Lesion changes less than 3 voxels were excluded.

Statistical analysis. A neuroradiologist reviewed FLAIR and subtraction images with overlaid color boxes encompassing the detected lesion changes (Fig.3). These were labeled as “true positive” or “false positive”. The reader also reviewed the images outside of these boxes to count the number of missed lesion changes (“false negative”) and unchanged lesions (“true negative”).

### RESULTS

Figure 3 shows an example of lesion detection obtained with LPA and proposed SDC algorithms. LPA was oversensitive and generated a much higher number of false positives than SDC. LPA also missed small lesions. Over 30 subjects, our SDC algorithm detected 344 lesion changes or 11±7 per subject on average (range 4-33), while LPA detected 1506 changes or 50±38 per subject (range 5-152). Despite a much-reduced number of detected changes, the SDC algorithm missed only 1 lesion vs. 24 misses by LPA. Our SDC algorithm achieved a sensitivity/specificity of 99%/76%, which outperformed LPA (76%/27%).

### DISCUSSION

Our preliminary data show that the proposed SDC algorithm can be a valuable computer-assisted tool to improve MS lesion detection and reduce reader’s fatigue. While only positive change (lesion growth) was considered, the detection of negative change can be done by swapping the order of source images. Further evaluation on patient data is warranted, particularly in those with large brain anatomy changes between scans which can interfere with subtraction.

### CONCLUSION

The proposed SDC detection algorithm has high sensitivity/specificity and performs better than LPA algorithm.

### Acknowledgements

This study was supported in part by grants from the NIH (R01NS090464) and the National MS Society (RG-1602-07671).

### References

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2. Moraal B, Wattjes MP, Geurts JJ, Knol DL, van Schijndel RA, Pouwels PJ, Vrenken H, Barkhof F. Improved detection of active multiple sclerosis lesions: 3D subtraction imaging. Radiology. 2010 Apr;255(1):154-63.

3. van Heerden J, Rawlinson D, Zhang AM, Chakravorty R, Tacey MA, Desmond PM, Gaillard F. Improving Multiple Sclerosis Plaque Detection Using a Semiautomated Assistive Approach. JNR Am J Neuroradiol. 2015 Aug;36(8):1465-71.

4. Battaglini M, Rossi F, Grove RA, Stromillo ML, Whitcher B, Matthews PM, De Stefano N. Automated identification of brain new lesions in multiple sclerosis using subtraction images. J Magn Reson Imaging. 2014 Jun;39(6):1543-9.

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6. Filippi M, Rocca MA, Ciccarelli O, De Stefano N, Evangelou N, Kappos L, Rovira A, Sastre-Garriga J, Tintorè M, Frederiksen JL, Gasperini C0, Palace J1, Reich DS2, Banwell B3, Montalban X, Barkhof F; MAGNIMS Study Group. MRI criteria for the diagnosis of multiple sclerosis: MAGNIMS consensus guidelines. Lancet Neurol. 2016 Mar;15(3):292-303.

7. Jenkinson M, Beckmann CF, Behrens TE, Woolrich MW, Smith SM. FSL. Neuroimage. 2012 Aug 15;62(2):782-90.

8. Paul Schmidt. Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging. PhD thesis, Ludwig-Maximilians-Universität München, January 2017. URL http://nbn-resolving.de/urn:nbn:de:bvb:19-203731.

### Figures

Figure 1. Schematic of the proposed SDC algorithm for lesion change detection on FLAIR subtraction image. The WM masks obtained from T1-weighted images by FSL are shown in red, which tend to exclude large bright lesions on FLAIR images and can be used to estimate the statistics of the unchanged image voxels on the FLAIR subtraction image and ultimately to compute the optimal threshold for the composite hypothesis test. In this example there is one unchanged (yellow arrow) and one new lesion (red), which are identified correctly by the algorithm.

Figure 2. Illustration of the 3-neighborhood of a voxel (center) to be used in the computation of the log-likelihood ratio test statistic in SDC algorithm. Each group contains 3 connected voxels as indicated by the green lines. There are a total of 6 groups in this 2D example and 15 groups in 3D (used in the study).

Figure 3. Example of changed lesions identified by LPA and proposed SDC algorithms. LPA is oversensitive and picks up more false positives (yellow arrow), yet still misses a new small lesion (red arrow). SDC correctly classifies the positive lesion changes.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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